A particle starts moving along a line from zero initial velocity and comes to rest after moving distance d. During its motion it had a constant acceleration f over $2 / 3$ of the distance, and covered the rest of the distance with constant retardation. The time taken to cover the distance is

• A

  $\sqrt{2 \mathrm{~d} / 3 \mathrm{f}}$
• B

  $2 \sqrt{\mathrm{d} / 3 \mathrm{f}}$
• Correct answer
  C

  $\sqrt{3 \mathrm{~d} / \mathrm{f}}$
• D

  $\sqrt{3 \mathrm{~d} / 2 \mathrm{f}}$

Solution

$\mathrm{a}_{1} l_{1}=\mathrm{a}_{2} l_{2}$ by equation of motion $\begin{array}{l} \text { Retardation }=2 f \\ t=t_{1}+t_{2} \\ =\sqrt{\frac{4 d}{3 f}}+\sqrt{\frac{2 d}{2 f}}=\sqrt{\frac{3 d}{f}} \end{array}$

Hence, the correct answer is option: 'C'.